Modified Runge-Kutta methods for the numerical solution of ODEs with oscillating solutions

Abstract

Three new modified Runge-Kutta methods with minimal phase-lag are developed for the numerical solution of ordinary differential equations with oscillating solutions. These methods are based on the well-known Runge-Kutta method of Dormand and Prince RK5(4)T (see [1]) of order five. Numerical and theoretical results show that this new approach is more efficient compared with the well known classical fifth-order Runge-Kutta Dormand and Prince method.